Q33 / 75 · JEE Main 2026 (05 April Shift 1) · Mathematics

The mean deviation about the mean for the data
$x_i$$5$$7$$9$$10$$12$$15$
$f_i$$8$$6$$2$$2$$2$$6$
is equal to:

  • A
    $\dfrac{40}{13}$
  • B
    $\dfrac{42}{13}$
  • Correct answer
    C
    $\dfrac{44}{13}$
  • D
    $\dfrac{46}{13}$

Solution

Mean $\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i}$

$\sum f_i = 8 + 6 + 2 + 2 + 2 + 6 = 26$

$\sum f_i x_i = 8(5) + 6(7) + 2(9) + 2(10) + 2(12) + 6(15)$

$\sum f_i x_i = 40 + 42 + 18 + 20 + 24 + 90 = 234$

$\bar{x} = \dfrac{234}{26} = 9$

Mean deviation about mean $= \dfrac{\sum f_i |x_i - \bar{x}|}{\sum f_i}$

$\sum f_i |x_i - \bar{x}| = 8|5 - 9| + 6|7 - 9| + 2|9 - 9| + 2|10 - 9| + 2|12 - 9| + 6|15 - 9|$

$\sum f_i |x_i - \bar{x}| = 8(4) + 6(2) + 2(0) + 2(1) + 2(3) + 6(6)$

$\sum f_i |x_i - \bar{x}| = 32 + 12 + 0 + 2 + 6 + 36 = 88$

Mean deviation $= \dfrac{88}{26} = \dfrac{44}{13}$

Answer: $\dfrac{44}{13}$

Hence, the correct answer is option: 'C'.

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